Just as in convex problems, can a non-convex minimization algorithm be used as a maximization algorithm by flipping the sign of the objective function? I am referring to the algorithm in https://link.springer.com/article/10.1007/s10107-017-1206-8.
Please excuse me if the question is too high level. I am just beginning to understand the whole concept of optimization. The book from prof. Boyd on convex optimization says this 'sign flipping' can be done. Wanted to know if it is true for the problem similar to the one mentioned in the above article.
Thanks a lot
We say that $x^\star$ is a (global) maximizer of $f$ if for all $x$, $f(x^\star)\geq f(x)$. This is equivalent to saying that for all $x$, $-f(x^\star)\leq -f(x)$, which means that $x^\star$ is a minimizer of the function $-f$. So yes, this "sign flipping" can be done both for convex and non-convex functions since the convexity of $f$ is never used in the above proof.